The generator matrix

 1  0  1  1  1  1  1  1  0  1 2X^2  1  1  1  1  X  1  1  1  1  1  1  1 2X^2+X  1  1  0 X^2+2X  1  1  1 X^2+X 2X^2+2X  1  1  1  1  1 2X^2+X  1 X^2+X  1  1  1  1 2X  1  1 2X^2  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  0 2X^2+X  1  X  1  1 2X^2+2X  1 2X
 0  1  1  2 2X^2+X 2X^2+X+2 2X^2+2X+1 2X  1 2X^2+X+1  1 2X^2+2 2X+2 X+1 2X^2  1 2X+2 2X^2+2X X+1 2X^2+1 2X^2+2X+2 X^2 2X+1  1 X^2+2 X^2+2X  1  1 X^2+X+2 X^2+X 2X^2+2X+1  1  1 X+2 2X^2+X 2X+1  1 2X^2+X+2  1 2X+2  1 2X^2+2X 2X^2+X 2X^2 2X  1 X+2 2X^2+1  1 2X^2+X X^2+X+1 2X^2+1 X+1 X^2  1 2X^2+1 X^2+X X^2+X+1 X^2+2X+1 2X^2 X^2 2X^2+2X+1 2X^2+2X+1  2 2X^2+2X  1 2X^2+1 X^2+2X+2  1  1  1 X^2+X+2 X^2+2X  0 X^2+1  1 2X^2+X+2  1
 0  0 2X  0 2X^2 2X^2 X^2  0 X^2+2X 2X^2+X 2X^2+X 2X^2+X 2X^2+2X X^2+2X X^2+X 2X^2+X 2X^2 X^2+X X^2 2X^2 2X^2+X X^2+2X X^2+X 2X^2 2X 2X^2+2X 2X 2X^2 2X X^2+X 2X X^2+2X  X 2X^2+X 2X^2+2X 2X^2+X X^2+X 2X 2X 2X^2+X  0 2X^2+2X X^2  0  X 2X^2+2X X^2 X^2+2X X^2+X X^2+2X 2X^2 X^2 2X^2+X  X  0 X^2 X^2+X 2X 2X^2+X X^2+2X 2X  0 X^2+2X 2X  0 X^2+X 2X X^2  X 2X 2X X^2+X X^2+2X X^2+X 2X^2  0 2X^2 X^2+2X
 0  0  0 X^2 X^2  0 2X^2 2X^2 2X^2 X^2 X^2  0  0 2X^2  0  0 2X^2 X^2  0 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2  0  0  0 X^2 2X^2 2X^2 2X^2  0 X^2 2X^2 2X^2  0  0 2X^2 X^2  0 X^2  0 2X^2 2X^2 2X^2  0 X^2 X^2 2X^2 2X^2 2X^2 X^2  0 X^2 X^2  0  0 2X^2 X^2  0 2X^2  0  0 2X^2  0 2X^2  0 X^2 X^2 2X^2 2X^2  0 X^2 X^2 X^2

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+276x^148+528x^149+728x^150+1314x^151+1494x^152+1100x^153+1902x^154+2052x^155+1362x^156+1866x^157+1968x^158+1304x^159+1278x^160+846x^161+544x^162+498x^163+342x^164+56x^165+66x^166+24x^167+2x^168+36x^169+30x^170+2x^171+24x^172+2x^174+24x^175+6x^179+6x^181+2x^183

The gray image is a linear code over GF(3) with n=702, k=9 and d=444.
This code was found by Heurico 1.16 in 2.33 seconds.